Question

perpendicular distance of the point p(3,5,6)from y-axis is​

Answer 1

Answer:

Since M is the foot of perpendicular from P on the y-axis therefore its x and z-coordinates are zero. The coordinates of M is 0 5 0. Therefore the perpendicular distance of the point P from y-axis √32 + 62 = 45 .

Answer 2

Given,

Point p(3, 5, 6).

To find,

Distance of the point from y-axis.

Solution,

Since on the y-axis, both the x- and z- coordinates will be 0.

The foot of the perpendicular from the given point will be (0, 5, 0). Now, we can find out the distance of p(3, 5, 6) from the y-axis using the distance formula. So the distance will be given by,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here, say

$(x_1,y_1,z_1)=(0,5,0),$ and,

$(x_2,y_2,z_2)=(3,5,6).$

So the distance,

$d=\sqrt{(3-0)^2+(5-5)^2+(6-0)^2}$

⇒ $d=\sqrt{(3)^2+0+(6)^2}$

⇒ $d=\sqrt{9+36}$

⇒ $d=\sqrt{45}$

⇒ d = 3√5 units.

Therefore, the perpendicular distance of the point p(3, 5, 6) from y-axis is 3√5 units.